Loading…

Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere

This paper is focused on efficient Monte Carlo simulations of Brownian diffusion effects in particle-based numerical methods for solving transport equations on a sphere (or a circle). Using the heat equation as a model problem, random walks are designed to emulate the action of the Laplace–Beltrami...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and computation 2020-01, Vol.364, p.124670, Article 124670
Main Authors: Novikov, A., Kuzmin, D., Ahmadi, O.
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is focused on efficient Monte Carlo simulations of Brownian diffusion effects in particle-based numerical methods for solving transport equations on a sphere (or a circle). Using the heat equation as a model problem, random walks are designed to emulate the action of the Laplace–Beltrami operator without evolving or reconstructing the probability density function. The intensity of perturbations is fitted to the value of the rotary diffusion coefficient in the deterministic model. Simplified forms of Brownian motion generators are derived for rotated reference frames, and several practical approaches to generating random walks on a sphere are discussed. The alternatives considered in this work include projections of Cartesian random walks, as well as polar random walks on the tangential plane. In addition, we explore the possibility of using look-up tables for the exact cumulative probability of perturbations. Numerical studies are performed to assess the practical utility of the methods under investigation.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2019.124670